Wolfgang Schwarz :: Non-rigid atomic expressions

Non-rigid atomic expressions

Posted on Thursday, 22 Mar 2007.

I gave a talk about the Canberra Plan on Tuesday (slides) in which I mentioned that I disagree with Lewis and Kim about the semantics of "pain": they say "pain" denotes whatever occupies the pain role in the species under consideration (or whatever is the relevant kind); I think "pain" rather denotes the property of being in a state that realises the pain role. One of the reasons I gave for my preference is that "pain" would be rather exceptional if it worked as Lewis and Kim believe.

What would be exceptional is that "pain" would not only be context-dependent but also index-dependent, i.e. non-rigid. Lewis explicitly says that "pain" is non-rigid in "Reduction of Mind", and I think this is required on his view to account for some of the things we say, like

1) it is possible that all animals in a world have pain, even though they do not all belong to a common species,

2) there are possible worlds where we have pain but are in a different brain state than we are when we actually have pain.

Here it seems that the reference of "pain" would have to vary between indices of evaluation.

There clearly are non-atomic expressions that behave like this: "the state that plays the pain role", "the closing mechanism", "the door", "my bike". These are all non-rigid and display both context-dependence and index-dependence. But I think this is entirely due to the occurrences of "the" and "my". I can't think of any atomic expressions in English (or German) that clearly behave like these complex expressions do.

(If there aren't any such expressions, 2D semantics in a sense leaves far too much freedom. When we learn a word, we learn its application conditions across counteractual situations; we never have to learn a full 2D matrix. The matrix automatically falls out of the diagonal.)

However, there are some unclear cases. Andy Egan mentioned "tall". It is certainly context-dependent. Is it also index-dependent?

3) If everybody were much taller than I, I wouldn't be tall.

That sounds okay. But it is easy to confuse index-variation with context-variation in such cases. (Compare "if 'leg' meant tail...".) Surely in the envisaged situation I would not be called tall, but I might still satisfy what is expressed by "tall" in the utterance context. As Weng Hong pointed out, it doesn't seem that I would suddenly become very tall just because everybody who is taller than me died (even though I might then come to be called tall). Moreover, this is certainly true:

4) it is possible that everybody be tall.

In a world where (4) is true, even the smallest person is tall. (I assume that some of the worlds that make (4) true have a smallest person.) Here the standards for "tall" do not appear to be set by the world of evaluation.

On the other hand, I don't know how to handle sentences like

5) if the sizes of the members of all species varied considerably, then every species would have members that are tall and others that are small,

which at least doesn't sound obviously false. Does it require index-variation or some semantic equivalent (such as assigning "tall" a hidden argument place for a pair of a contrast class and a world)?

Another worry (that Daniel Nolan brought up) is that if the behaviour of "tall" (and "funny" and "tasty" etc.) can be fully explained without index-dependence, then perhaps this explanation could be applied to the Lewis-Kim interpretation of "pain" as well.

What do you think? Are there good reasons to treat "tall" as index-dependent, or are there other candidates for atomic index-dependent expressions? And are there good tests for index-dependence that I'm missing?

Comments

# Dan LÃ³pez de Sa on 22 March 2007, 13:14

Very interesting!

Just a side remark: I wasn't completely clear about the reason why you think that the non-rigidty claim is required on Lewis' view to account for things such as (1) and (2) above. Assume that expressions such as 'has pain' refer (wrt an index) to properties. Stipulate that 'has pain-1' non-rigidly refers wrt to the different indices to the different properties that play the pain-role in these indices (Ã la Lewis). Consider now the property that is had by something at an index iff the thing has the property 'has pain-1' non-rigidly refers to wrt that index. And stipulate that 'has pain-2' rigidly refers to that property. It seems to me that (1) and (2) would be as much true with 'have pain-1' in the place of 'have pain' as they would be with 'have pain-2' instead.

# wo on 23 March 2007, 02:36

Thanks Dan! I'm afraid I don't quite understand the question, but perhaps that's because I was a bit cryptic at that point. Isn't "pain-1" what Lewis believes "pain" to be (a non-rigid term for whatever plays the pain role) and "pain-2" what I believe it to be (a rigid expression for the property of being in a state that occupies the pain role)? If so, I think you're right that (1) and (2) come out true either way. But Lewis argues that "pain" is not "pain-2", because by analytical necessity, pain is what occupies the pain role. So the Lewisian alternative I had in mind was to say that "pain" rigidly refers to what occupies the pain role in whatever species is relevant in the utterance context. And on this view, (1) and (2) seem to become false.

# Dan LÃ³pez de Sa on 23 March 2007, 16:45

Thanks for this, Wo. I thought you thought that (1) and (2) being true required the non-rigid claim, but now I see we agree that they do not.

And the more general issue you raise, of whether there are any plausible candidates of non-rigid atomic expressions, is very interesting indeed. What are you inclined to say about 'is funny' or 'is tasty'?

# M. on 23 March 2007, 21:56

wo,
Forgive me but for a beginner this post started like it was a (interesting or boring) discussion about the difference between:
(1) "X" denotes the X role
(2) "X" denotes the property of being in a state that realises the X role
where (2) patently looks pleonastic.

Where is the smart turn when this relates to context-, index-dependence and rigidity?

# wo on 24 March 2007, 03:23

Dan, I wish I had a clear grasp of "funny" and "tasty" (and "difficult"). I'm inclined to say that they rigidly express the property of being disposed to be found funny/tasty by the speaker or whoever is relevantly salient in the utterance context. "(Ey) x is funny for y" then does not entail "x is funny"; it is more like "(Ey) x is funny according to y". But maybe they really express relations, like "is taller": "for any bird, there is some elephant that is taller" seems to be shorthand for "for any bird, there is some elephant that is taller *than this bird*".

M, the first option I have in mind is not quite yours. The choice is:

(1) "X" denotes the occupant of the X role;

(2) "X" denotes the property of being in a state that occupies the X role,

Lewis insists that for "pain", (1) is correct. The question then arises about what to say if different things occupy the X role in different species and in different worlds. Lewis's response is that the denotation of "X" shifts with the index of evaluation. So in a sentence like "at some world w, humans have pain when their D-fibres fire", the denotation of "pain" at every considered world w would be the occupant of the pain role in humans at w. This is index-variation, not simply context-variation. Descriptors like "the occupant of the pain role" clearly display this behaviour, but atomic expressions usually don't: their denotation remains constant within modal (or other index-shifting) contexts.

# Dan LÃ³pez de Sa on 24 March 2007, 12:55

I thought you might have been inclined to take another view on âis funny/tasty,â more similar to the one you suggest with respect to âhas pain,â and which is the kind of view I would myself favor regarding evaluative predicates in general.

Assume for simplicity that worlds are the only coordinates of indices, and that âthe speakerâ refers to whoever is relevantly salient in the conversation that takes place at the center of the context (if such there is). The âLewisian/flexibilityâ view would then have it that âis funny/tastyâ at c refers rigidly to the âflexibleâ property that is had by something at a world w iff âthe speakerâ of c is disposed in w to find it funny/tasty. This would account for the fact that, as someone put it, we would not take very seriously the suggestion that something which is actually funny would continue to be funny even if a comprehensive alteration in our comic sensibilities took place.

I wasnât there, but this may be related to the point you report Daniel made in your discussion. If something like this were to work, perhaps (pace Lewis) the corresponding thing can be made to work with respect to âhas pain,â doesnât it?

# wo on 25 March 2007, 13:44

hm, this "Lewisian/flexibility" view doesn't look like Lewis's view on "pain" to me: according to Lewis, "pain" is a non-rigid designator that picks out different physical states/properties at different worlds. But your proposal is also interesting; I hadn't thought about this possibility. Though I would not like to claim that things are only funny in worlds where I exist. Isn't that rather odd?

Wolfgang Schwarz

Non-rigid atomic expressions

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